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Horiuchi Toshio  堀内 利郎

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… Alternative Names

HORIUCHI Toshio  堀内 利郎

堀内 利郎  ホリウチ トシオ

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Researcher Number 80157057
Other IDs
External Links
Affiliation (Current) 2020: 茨城大学, 理工学研究科(理学野), 教授
Affiliation (based on the past Project Information) *help 2018 – 2020: 茨城大学, 理工学研究科(理学野), 教授
1995 – 2017: 茨城大学, 理学部, 教授
2005: 茨成大学, 理学部, 教授
1996: 茨城大学 理学部, 教授
1994: 茨城大学, 理学部, 助教授
1991: 茨城大学, 理学部, 助教授
1987: 茨城大学, 理学部, 助手
Review Section/Research Field
Principal Investigator
Basic analysis / 解析学 / Basic analysis / Basic Section 12020:Mathematical analysis-related
Except Principal Investigator
Basic analysis / 解析学 / Basic analysis
Keywords
Principal Investigator
退化楕円型方程式 / 非線形楕円型方程式 / ソボレフの不等式 / 重み付きソボレフ不等式 / CKN型不等式 / ソボレフ不等式 / ハーディ不等式 / ミッシングターム / 重み付きソボレフの不等式 / degenerate elliptic equation … More / ハーディーの不等式 / P-harmonic / 重み付きハーディ不等式 / ミッシング・ターム / 変分問題 / 加藤の不等式 / 強最大値原理 / ハーディの不等式 / CKN 型不等式 / p-ラプラシアン / 解の正則性 / 特異点の除去 / ポテンシャル論 / 特異点の除去可能性 / うめ込み定理 / Sobolev inequality / 非線型楕円型方程式 / Hardy inequality / 特異解 / P-調和作用素 / 最小解 / singular solution / Rellich inequality / missing terms / クリティカル・イクスポ-ネント / ベスト・コンスタント / 重み付きソボレフの埋め込み定理 / 重み付きソボレ不等式 / 非線形変分問題 / 楕円型偏微分方程式 / 退化楕円型問題 / 対称性の破れ / 退化楕円型 / バーディ不等式 / CKN型不等式 / 楕円型変分問題 / p-ラプラシアン / 対称性の崩れ / Super logarithm / 重み付きハーディの不等式 / ミッシンク・ターム / Hardy-Sobolevの 不等式 / Hardyの不等式の精密化 / スーパー対数関数 / 不等式の精密化 / 超対数関数 / 不等式のミッシングターム / 退化型非線形偏微分方程式 / ソボレフのうめ込み定理 / キャパシティ / 解の有界性 / 解の数値解析 / regularity / removable singularity / P調和方程式 / 非線型楕円型 / ハーディー不等式 / p調和方程式 / 非線形楕円型 / 除去可能な特異点 / degeneration alliptic / Singularity / potential theory / non-linear eliptic / 非線形楕円型作用素 / レリッヒの不等式 / 退化楕円型方程式n / P-調和方程式 / nonlinear elliptic equation / minimal solution / 線形化問題 / レリッヒ不等式 / バーディの不等式 / p調和作用素 / 最良定数 / weighted Sobolev ineauality / linearization / Hardy ineouality / 逆最大値原理 / 非線型変分問題 / 非線形楕円型変分問題 / 退化楕円型偏微分方程式 / 重み付きHardy 不等式の精密化 / 重み付きSobolev不等式の精密化 / CKN型不等式の精密化 / 非線形退化楕円型変分問題 / 加藤の不等式の精密化 … More
Except Principal Investigator
caloric morphism / 熱方程式の解を保つ変換 / Appell変換 / 熱方程式 / 調和解析 / 関数空間 / Appell transformation / heat equation / ウェーブレット / 実解析 / 波動方程式の解を保つ変換 / Bateman変換 / 変動指数 / Hardy空間 / 作用素 / 代作用代数 / エントロピ- / Toeplitz作用素 / Schrodinger / ポテンシャル / 相対容量 / シュタルク効果 / 波動作用素 / 漸近的完全性 / 散乱全断面積 / 準古典近似 / 影散乱 / フォン・ノイマン環 / 因子環 / 非可換力学系 / 非可換確率論 / 非可換エントロピー / ランダム・ウォーク / 自由確率論 / 多重線形 / 多重線形作用素 / ベイトマン変換 / 調和解析学 / 実解析学 / 分数べき積分 / 特異積分 / Orlicz空間 / Campanato空間 / Morrey空間 / Hardy-Orlicz族 / BMO / 特異積分作用素 / 埋め込み定理 / 多重熱作用素の解 / ソボレフ空間 / 重み付き空間 / Triebel-Lizorkin空間 / 非線型波動方程式 / 非線型変分問題 / Sobolev-Lieb-Thirring不等式 / 非線型方程式 / シュレディンガー方程式 / Sobolev space / wavelet / weighted space / Triebel-Lizorkin space / 積分作用素 Less
  • Research Projects

    (24 results)
  • Research Products

    (95 results)
  • Co-Researchers

    (36 People)
  •  A new refinement allowing infinite-order degeneration and explosion of weighted classical inequalities and its application to variational problemsPrincipal InvestigatorOngoing

    • Principal Investigator
      堀内 利郎
    • Project Period (FY)
      2020 – 2024
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Review Section
      Basic Section 12020:Mathematical analysis-related
    • Research Institution
      Ibaraki University
  •  古典的不等式の精密化に基づく非線型楕円型方程式の定性的研究Principal InvestigatorOngoing

    • Principal Investigator
      堀内 利郎
    • Project Period (FY)
      2016 – 2019
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Ibaraki University
  •  実解析・調和解析に由来する関数空間の理論の深化と応用Ongoing

    • Principal Investigator
      中井 英一
    • Project Period (FY)
      2015 – 2019
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Basic analysis
    • Research Institution
      Ibaraki University
  •  Research on transformations preserving solutions of the heat equation, wave equation

    • Principal Investigator
      Shimomura Katsunori
    • Project Period (FY)
      2013 – 2015
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Ibaraki University
  •  Refinement of classical inequalities and its application to elliptic variational problemsPrincipal Investigator

    • Principal Investigator
      Horiuchi Toshio
    • Project Period (FY)
      2012 – 2015
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Ibaraki University
  •  Harmonic analysis based on function spaces with variable exponent and its applications

    • Principal Investigator
      NAKAI Eiichi
    • Project Period (FY)
      2012 – 2014
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Ibaraki University
  •  The research of transformations which preserve the solutions of the heat equation and the wave equation.

    • Principal Investigator
      SHIMOMURA Katsunori
    • Project Period (FY)
      2010 – 2012
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Ibaraki University
  •  Reseach on multilinear harmonic analysis and its applications

    • Principal Investigator
      TACHIZAWA Kazuya
    • Project Period (FY)
      2008 – 2011
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Hokkaido University
  •  On the improvement of classical inequalities and its applications to nonlinear degenerate elliptic equationsPrincipal Investigator

    • Principal Investigator
      HORIUCHI Toshio
    • Project Period (FY)
      2008 – 2011
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Ibaraki University
  •  The research of caloric morphism

    • Principal Investigator
      SHIMOMURA Katsunori
    • Project Period (FY)
      2007 – 2008
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Ibaraki University
  •  The Study of caloric morphism

    • Principal Investigator
      SHIMOMURA Katsunori
    • Project Period (FY)
      2005 – 2006
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Ibaraki University
  •  On the linearization of quasilinear degenerate elliptic equations and the structure of singular solutionsPrincipal Investigator

    • Principal Investigator
      HORIUCHI Toshio
    • Project Period (FY)
      2005 – 2007
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Ibaraki University
  •  A characterization of weighted Sobolev spaces and its applications

    • Principal Investigator
      TACHIZAWA Kazuya
    • Project Period (FY)
      2004 – 2006
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Hokkaido University
  •  The research of caloric morphism

    • Principal Investigator
      SHIMOMURA Katsunori
    • Project Period (FY)
      2003 – 2004
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      IBARAKI UNIVERSITY
  •  On the structure of singular solutions for degenerate elliptic equationsPrincipal Investigator

    • Principal Investigator
      HORIUCHI Toshio
    • Project Period (FY)
      2002 – 2004
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      IBARAKI UNIVERSITY
  •  The research of caloric morphism

    • Principal Investigator
      SHIMOMURA Katsunori
    • Project Period (FY)
      2001 – 2002
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      IBARAKI UNIVERSITY
  •  The research on degenerate elliptic partial differential equations by the method of real analysisPrincipal Investigator

    • Principal Investigator
      HORIUCHI Toshio
    • Project Period (FY)
      1999 – 2001
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      IBARAKI UNIVERSITY
  •  On the regularity of solutions for degenerate elliptic equationsPrincipal Investigator

    • Principal Investigator
      HORIUCHI Toshio
    • Project Period (FY)
      1997 – 1998
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      IBARAKI UNIVERSITY
  •  作用素環上の非可換確率論の研究

    • Principal Investigator
      日合 文雄
    • Project Period (FY)
      1996
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Ibaraki University
  •  退化楕円型方程式の解の構造の研究Principal Investigator

    • Principal Investigator
      堀内 利郎
    • Project Period (FY)
      1996
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Ibaraki University
  •  退化楕円型方程式に関する諸問題の研究Principal Investigator

    • Principal Investigator
      堀内 利郎
    • Project Period (FY)
      1995
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Ibaraki University
  •  シュレ-ディンガー作用素のスペクトル理論の研究

    • Principal Investigator
      田村 英男
    • Project Period (FY)
      1994
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Ibaraki University
  •  作用素解析と作用素代数の研究

    • Principal Investigator
      日合 文雄
    • Project Period (FY)
      1991
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Ibaraki University
  •  複素構造に関連した解析学の研究

    • Principal Investigator
      荷見 守助
    • Project Period (FY)
      1987
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Ibaraki University

All 2019 2018 2017 2016 2015 2014 2012 2010 2009 2008 2007 2006 2005 2004 2003 Other

All Journal Article Presentation Book

  • [Book] 関数解析の基礎2005

    • Author(s)
      堀内利郎
    • Total Pages
      280
    • Publisher
      内田老鶴圃
    • Data Source
      KAKENHI-PROJECT-14540151
  • [Book] 関数解析の基礎2005

    • Author(s)
      堀内利郎
    • Total Pages
      296
    • Publisher
      内田老鶴圃
    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-17540146
  • [Journal Article] Kato’s inequalities for admissible functions to quasilinear elliptic operators A2019

    • Author(s)
      Xiaojing Liu, Toshio Horiuchi
    • Journal Title

      Mathematical journal of ibaraki University

      Volume: 51

    • NAID

      130007687047

    • Peer Reviewed / Open Access / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-16K05189
  • [Journal Article] The equivalences among p-capacity, $p$-Laplace-capacities and Hausdorff measure.2018

    • Author(s)
      Xiaojing Liu, Toshio Horiuchi
    • Journal Title

      Mathematical Journal of Ibaraki University Volume

      Volume: 50

    • NAID

      130007465434

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-16K05189
  • [Journal Article] The equivalences among <i>p</i>-capacity, <i>p</i>-Laplace-capacities and Hausdorff measure2018

    • Author(s)
      Liu Xiaojing、Horiuchi Toshio
    • Journal Title

      Math. J. Ibaraki Univ.

      Volume: 50 Issue: 0 Pages: 5-13

    • DOI

      10.5036/mjiu.50.5

    • NAID

      130007465434

    • ISSN
      1343-3636, 1883-4353
    • Language
      English
    • Peer Reviewed / Open Access / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-16K05189
  • [Journal Article] The equivalences among p-capacity, p-Laplace-capacities and Hausdorff measure.2018

    • Author(s)
      Liu Xiaojing、Horiuchi Toshio
    • Journal Title

      Mathematical Journal of Ibaraki University

      Volume: 50

    • NAID

      130007465434

    • Peer Reviewed / Open Access
    • Data Source
      KAKENHI-PROJECT-15H03621
  • [Journal Article] Remarks on the strong maximum principle involvingp-Laplacian2016

    • Author(s)
      Xiaojing Liu, Toshio Horiuchi
    • Journal Title

      Hiroshima Mathematical Journal

      Volume: 46 Pages: 311-331

    • Peer Reviewed / Acknowledgement Compliant / Open Access / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-16K05189
  • [Journal Article] Remarks on the strong maximum principle involving p-Laplacian2016

    • Author(s)
      Xiaojing Liu and Toshio Horiuchi
    • Journal Title

      Hiroshima Mathematical Journal

      Volume: 46

    • Peer Reviewed / Acknowledgement Compliant / Open Access
    • Data Source
      KAKENHI-PROJECT-15H03621
  • [Journal Article] Remarks on Kato's inequality when $\Delta_p u$ is a measure2016

    • Author(s)
      Xiaojing Liu and Toshio Horiuchi
    • Journal Title

      Mathematical Journal of Ibaraki University

      Volume: 48

    • Peer Reviewed / Open Access
    • Data Source
      KAKENHI-PROJECT-15H03621
  • [Journal Article] Caffarelli-Kohn-Nirenberg 型不等式とその周辺2016

    • Author(s)
      堀内利郎
    • Journal Title

      数学(日本数学会)

      Volume: 68 Pages: 1-23

    • NAID

      130006321022

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-24540157
  • [Journal Article] Radial symmetry and its breaking in the Caffarelli-Kohn- Nirenberg type inequalities2016

    • Author(s)
      Naoki. Chiba, Toshio. Horiuchi
    • Journal Title

      Proceedings of the Japan academy

      Volume: 92 (4) Pages: 51-55

    • DOI

      10.3792/pjaa.92.51

    • Peer Reviewed / Acknowledgement Compliant
    • Data Source
      KAKENHI-PROJECT-16K05189
  • [Journal Article] Remarks on Kato's inequality when $\Delta_p u$ is a measure2016

    • Author(s)
      Xiaojing Liu, Toshio Horiuchi
    • Journal Title

      Mathematical Journal of Ibaraki University

      Volume: 48 Pages: 45-61

    • Peer Reviewed / Acknowledgement Compliant / Open Access / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-16K05189
  • [Journal Article] radial symmetry and its breaking in the Caffarelli-Kohn-Nirenberg type inequalities for p=12016

    • Author(s)
      N. Chiba, T. Horiuchi
    • Journal Title

      Proceedings of the Japan academy Series A Mathematical Sciences

      Volume: 92 Pages: 51-55

    • NAID

      130005100042

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-24540157
  • [Journal Article] Caffarelli-Kohn-Nirenberg 型不等式とその周辺2016

    • Author(s)
      堀内利郎
    • Journal Title

      数学

      Volume: 68

    • NAID

      130006321022

    • Peer Reviewed / Open Access
    • Data Source
      KAKENHI-PROJECT-15H03621
  • [Journal Article] On radial symmetry and its breaking in the Caffarelli-Kohn-Nirenberg type inequalities for p=12015

    • Author(s)
      N. Chiba, T. Horiuchi
    • Journal Title

      Mathematical Journal of Ibaraki University

      Volume: 47 Pages: 49-63

    • NAID

      130005100042

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-24540157
  • [Journal Article] Some properties of slowly increasing functions2014

    • Author(s)
      Ando Hiroshi, Horiuchi Toshio, Nakai eiichi
    • Journal Title

      Mathematical Journal of Ibaraki University

      Volume: 46 Pages: 37-49

    • NAID

      130004697043

    • Peer Reviewed / Acknowledgement Compliant / Open Access
    • Data Source
      KAKENHI-PROJECT-24540157
  • [Journal Article] Some properties of slowly increasing functions2014

    • Author(s)
      Hiroshi Ando, Toshio Horiuchi and Eiichi Nakai
    • Journal Title

      Mathematical Journal of Ibaraki University

      Volume: 46

    • NAID

      130004697043

    • Peer Reviewed / Acknowledgement Compliant / Open Access
    • Data Source
      KAKENHI-PROJECT-24540159
  • [Journal Article] Weighted Hardy inequalities with infinitely many sharp missing terms2014

    • Author(s)
      Ando, Hiroshi; Horiuchi, Toshio; Nakai
    • Journal Title

      Mathematical Journal of Ibaraki University

      Volume: 48 Pages: 9-29

    • NAID

      130004697044

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-24540157
  • [Journal Article] Weighted Hardy inequalities with infinitely many sharp missing terms2014

    • Author(s)
      Hiroshi Ando, Toshio Horiuchi and Eiichi Nakai
    • Journal Title

      Mathematical Journal of Ibaraki University

      Volume: 46

    • NAID

      130004697044

    • Peer Reviewed / Acknowledgement Compliant / Open Access
    • Data Source
      KAKENHI-PROJECT-24540159
  • [Journal Article] Weighted Hardy inequalities with infinitely many sharp missing terms2014

    • Author(s)
      Ando Hiroshi, Horiuchi Toshio, Nakai eiichi
    • Journal Title

      Mathematical Journal of Ibaraki University

      Volume: 46 Pages: 9-30

    • NAID

      130004697044

    • Peer Reviewed / Acknowledgement Compliant / Open Access
    • Data Source
      KAKENHI-PROJECT-24540157
  • [Journal Article] Construction of slowly increasing functions2012

    • Author(s)
      Hiroshi Ando, Toshio Horiuchi and Eiichi Nakai
    • Journal Title

      Scientiae Mathematicae Japonicae

      Volume: 75

    • NAID

      130007663411

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-24540159
  • [Journal Article] Peter Kumlin, On the Caffarelli-Kohn-Nirenberg-type inequalities involving critical and supercritical weights2012

    • Author(s)
      堀内利郎
    • Journal Title

      Kyoto Journal of Mathematics

      Volume: 52 Pages: 661-742

    • URL

      http://projecteuclid.org/euclid.kjm/1352987531

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-22540169
  • [Journal Article] The Caffarelli-Kohn-Nirenberg inequalities involving critical and supercritical weights2012

    • Author(s)
      T.Horiuchi, P.Kumlin
    • Journal Title

      Proceedings of the Japan Academy

      Volume: 88 Pages: 1-6

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20540153
  • [Journal Article] The Caffarelli-Kohn-Nirenberg inequalities involving critical and supercritical weights2012

    • Author(s)
      T. Horiuchi, P. Kumulin
    • Journal Title

      Proceedings of the Japan Academy

      Volume: Vol.88, Ser. A No.1 Pages: 1-6

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20540153
  • [Journal Article] The Caffarelli-Kohn-Nirenberg type inequalities involving critical and supercritical weights, Proc.2012

    • Author(s)
      Toshio Horiuchi and Peter Kumlin
    • Journal Title

      Japan Acad. Ser.A Math. Sci

      Volume: 88(1) Pages: 1-6

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20540149
  • [Journal Article] CONSTRUCTION OF SLOWLY INCREASING FUNCTION2012

    • Author(s)
      H. Ando, T. Horiuchi, E. Nakai
    • Journal Title

      Scientiae Mathematicae Japonicae Online

      Volume: 25 Pages: 207-221

    • NAID

      130007663411

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-24540157
  • [Journal Article] Missing terms in the weighted Hardy-Sobolev inequalities and its application2012

    • Author(s)
      H. Ando, T. Horiuchi
    • Journal Title

      Kyoto Journal of Mathematics

      Volume: 52(4) Pages: 759-796

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-24540157
  • [Journal Article] On the weighted rearrangement of functions and Degenerate Nonlinear elliptic equations2012

    • Author(s)
      H. Ando, T. Horiuchi
    • Journal Title

      Mathematical Journal of Ibaraki University

      Volume: 44 Pages: 17-31

    • NAID

      130003373916

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-24540157
  • [Journal Article] Caffarelli-Kohn-Nirenberg inequalities involving critical and supercritical weights2012

    • Author(s)
      T.Horiuchi, P. Kumlin
    • Journal Title

      Kyoto Journal of Mathematics

      Volume: 52(4) Pages: 661-742

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-24540157
  • [Journal Article] Missing terms in the weighted Hardy-Sobolev inequalities and its application2012

    • Author(s)
      安藤広, 堀内利郎
    • Journal Title

      Kyoto Journal of Mathematics

      Volume: 52 Pages: 759-796

    • URL

      http://projecteuclid.org/euclid.kjm/1352987533

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-22540169
  • [Journal Article] Missing terms in the weighted Hardy-Sobolev inequalities and its application2010

    • Author(s)
      安藤広, 堀内利郎
    • Journal Title

      Journal of Mathematics of Kyoto Unuv.(accepted) (未定)

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20540153
  • [Journal Article] Missingterms in the weighted Hardy-Sobolev inequalities and its application2009

    • Author(s)
      安藤広、堀内利郎
    • Journal Title

      Journal of Mathematics of Kyoto Unuv. (accepted) (未定)

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20540153
  • [Journal Article] Missing terms in the weighted Hardy-Sobolev inequalities and its application2009

    • Author(s)
      安藤広、堀内利郎
    • Journal Title

      Journal of Mathematics of Kyoto University (巻頁未定)(印刷中)

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19540161
  • [Journal Article] Kato's inequalities for degenerate quasilinear elliptic operators2008

    • Author(s)
      T. Horiuchi
    • Journal Title

      Kungpook Mathematical J.

      Volume: 48-1 Pages: 15-24

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20540153
  • [Journal Article] Kato's inequalities for degenerate quasilinear elliptic operators2008

    • Author(s)
      堀内利郎
    • Journal Title

      Kyungpook Mathcmatical Journal 48-1

      Pages: 15-24

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-17540146
  • [Journal Article] Kato''s inequalities for degenerate quasilinear elliptic Operators2008

    • Author(s)
      T. Horiuchi
    • Journal Title

      Kyungpook Mathematical Journal 48-1

      Pages: 15-24

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-17540146
  • [Journal Article] Kato's inequalities for degenerate quasilinear elliptic operators2008

    • Author(s)
      堀内利郎
    • Journal Title

      Kyungpook Mathematical Journal 48

      Pages: 15-24

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19540161
  • [Journal Article] Kato's inequalities for degenerate quasilinear elliptic operators2008

    • Author(s)
      堀内利郎
    • Journal Title

      Kyungpook Mathematical Journal 48-1

      Pages: 15-24

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19540161
  • [Journal Article] Kato's inequalities for degenerate quasilinear lliptic operators2008

    • Author(s)
      Toshio Horiuchi
    • Journal Title

      Kyungpook Mathematical Journal

      Volume: 48(1) Pages: 15-21

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20540149
  • [Journal Article] Kato's inequalities for degenerate quasilinear elliptic operators2008

    • Author(s)
      堀内利郎
    • Journal Title

      Kyungpook Mathematical Journal 48-1

      Pages: 15-24

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-17540146
  • [Journal Article] Kato's inequalities for degenerate quasilinear elliptic operators2008

    • Author(s)
      Toshio Horiuchi
    • Journal Title

      Kyungpook Mathematical Journal 48(1)

      Pages: 15-24

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20540149
  • [Journal Article] Missing terms in Classical Inequalities2007

    • Author(s)
      T. Horiuchi
    • Journal Title

      Kyoto LTniv ersity. R. I. M. S. Koukyu_roku 1553

      Pages: 1-16

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-17540146
  • [Journal Article] Kato's Inequalities for Degenerate Quasilinear Elliptic Operators2007

    • Author(s)
      Horiuchi, Toshio
    • Journal Title

      Kyungpook Mathematical Journal (未定)

    • Data Source
      KAKENHI-PROJECT-17540146
  • [Journal Article] Missing terms in Classical Inequalities.2007

    • Author(s)
      堀内利郎
    • Journal Title

      数理解析研究所 講究録 1553

      Pages: 1-16

    • Data Source
      KAKENHI-PROJECT-17540146
  • [Journal Article] Missing terms in Classical Inequalites.2007

    • Author(s)
      堀内利郎
    • Journal Title

      数理解析研究所 講究録 1553

      Pages: 1-16

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-17540146
  • [Journal Article] Erratum to "On the minimal solution for quasilinear degenerate elliptic equation and its blow-up2006

    • Author(s)
      Horiuchi, Toshio
    • Journal Title

      Journal of Mathematics of Kyoto University 46-1

      Pages: 231-234

    • Data Source
      KAKENHI-PROJECT-17540146
  • [Journal Article] Erratum to "On the minimal solution for quasilinear degenerate elliptic equation and its blow-up2006

    • Author(s)
      堀内利郎
    • Journal Title

      Journal of Mathematics of Kyoto University (掲載決定)

    • Data Source
      KAKENHI-PROJECT-17540146
  • [Journal Article] Sharp remainder terms of Hardy-Sobolev inequalities.2005

    • Author(s)
      A.Detalla, T.Horiuchi, H.Ando
    • Journal Title

      Math.J.Ibaraki Univ. 37(印刷中)

    • NAID

      130000886481

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-15540153
  • [Journal Article] Sharp remainder terms of Hardy-Sobolev inequalities2005

    • Author(s)
      Alnar Detalla, Toshio Horiuchi, Hiroshi Ando
    • Journal Title

      Math.J.Ibaraki Univ. 37

      Pages: 39-52

    • NAID

      130000886481

    • Data Source
      KAKENHI-PROJECT-17540144
  • [Journal Article] Sharp Remainder terms of Hardy-Sobolev inequalities.2005

    • Author(s)
      A.Detalla, T.Horiuchi, H.Ando
    • Journal Title

      Math.J.Ibaraki Univ. 37

      Pages: 39-52

    • NAID

      130000886481

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-17540144
  • [Journal Article] Sharp remainder terms of Hardy-Sobolev inequalities2005

    • Author(s)
      Toshio Horiuchi
    • Journal Title

      Mathematical Journal Ibaraki University 37

      Pages: 39-52

    • NAID

      130000886481

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-16540133
  • [Journal Article] Sharp Remainder terms of Hardy-Sobolev inequalities.2005

    • Author(s)
      A.Detalla, T.Horiuchi, H.Ando
    • Journal Title

      Math.J.Ibaraki Univ. 37(to appear)

    • NAID

      130000886481

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-15540153
  • [Journal Article] Sharp Remainder terms of Hardy-Sobolev inequalities.2005

    • Author(s)
      A.Detalla, T.Horiuchi, H.Ando
    • Journal Title

      Math. J. Ibaraki Univ. 37

      Pages: 39-52

    • NAID

      130000886481

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-17540144
  • [Journal Article] Missing terms in Hardy-Sobolev inequalities and its application.2004

    • Author(s)
      A.Detalla, T.Horiuchi, H.Ando
    • Journal Title

      Far East Journal of Mathematical sciences 14(3)

      Pages: 333-359

    • Data Source
      KAKENHI-PROJECT-15540153
  • [Journal Article] On the minimal solution for quasilinear degenerate elliptic equation and its blow-up2004

    • Author(s)
      Toshio Horiuchi
    • Journal Title

      Journal of Kyoto Univ. 44・2

      Pages: 341-439

    • Data Source
      KAKENHI-PROJECT-16540133
  • [Journal Article] On the minimal solution for quasilinear degenerate elliptic equation and its blow-up2004

    • Author(s)
      堀内利郎
    • Journal Title

      Journal Math.Kyoto Univ. 44・2

      Pages: 341-439

    • Data Source
      KAKENHI-PROJECT-14540151
  • [Journal Article] On the minimal solution for quasilinear degenerate elliptic equation and its blow-up2004

    • Author(s)
      Toshio Horiuchi
    • Journal Title

      Journal of Mathematics Kyoto University 44

      Pages: 381-439

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-16540133
  • [Journal Article] Missing terms in Hardy-Sobolev inequalities and its application.2004

    • Author(s)
      A.Detalla, T.Horiuchi, H.Ando
    • Journal Title

      Far Fast Journal of Mathematical Sciences 14(3)

      Pages: 333-359

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-15540153
  • [Journal Article] Missing terms in Hardy-Sobolev inequalities.2004

    • Author(s)
      A.Detalla, T.Horiuchi, H.Ando
    • Journal Title

      Proc.of Japan Acad., Ser.A 80-8

      Pages: 160-165

    • NAID

      40006552680

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-15540153
  • [Journal Article] On the minimal solution for quasilinear degenerate elliptic equation and its blow-up2004

    • Author(s)
      堀内利郎
    • Journal Title

      Journal Math.Kyoto Univ. 44-2

      Pages: 341-439

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-14540151
  • [Journal Article] Missing terms in Hardy-Sobolev inequalities2004

    • Author(s)
      堀内利郎
    • Journal Title

      Proceedings of Japan Academy 80・A・8

      Pages: 160-165

    • NAID

      40006552680

    • Data Source
      KAKENHI-PROJECT-14540151
  • [Journal Article] On the minimal solution for quasilinear degenerate elliptic equation and its blow-up.2004

    • Author(s)
      T.Horiuchi, P.Kumlin
    • Journal Title

      J.of Kyoto Univ. 44-2

      Pages: 341-439

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-15540153
  • [Journal Article] On the minimal solution for quasilinear degenerate elliptic equation and its blow-up.2004

    • Author(s)
      T.Horiuchi
    • Journal Title

      J.of Kyoto Univ. 44-2

      Pages: 341-439

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-14540151
  • [Journal Article] Missing terms in Hardy-Sobolev inequalities.2004

    • Author(s)
      A.Detalla, T.Horiuchi, H.Ando
    • Journal Title

      Proceedings of Japan Academy 80Ser.A(8)

      Pages: 160-165

    • NAID

      40006552680

    • Data Source
      KAKENHI-PROJECT-15540153
  • [Journal Article] Missing terms in Hardy-Sobolev Inequalities and its application2004

    • Author(s)
      堀内利郎
    • Journal Title

      Far East Journal of Mathematical sciences(FJMS) 14・3

      Pages: 333-359

    • Data Source
      KAKENHI-PROJECT-14540151
  • [Journal Article] Missing terms in Hardy-Sobolev Inequalities and its application.2004

    • Author(s)
      A.Detalla, T.Horiuchi, H.Ando
    • Journal Title

      Far East J.Math.Sci.(FJMS) 14-3

      Pages: 333-359

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-15540153
  • [Journal Article] Missing terms in Hardy-Sobolev inequalities.2004

    • Author(s)
      A.Detalla, T.Horiuchi, H.Ando
    • Journal Title

      Proceedings of Japan Academy 80 Ser.A

      Pages: 160-165

    • NAID

      40006552680

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-15540153
  • [Journal Article] Missing terms in generalized Hardy inequalities and its application2003

    • Author(s)
      堀内利郎
    • Journal Title

      Journal Math.Kyoto Univ 43-2

      Pages: 235-260

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-14540151
  • [Journal Article] Missing terms in generalized Hardy's inequalities and its application2003

    • Author(s)
      T.Horiuchi
    • Journal Title

      J.of Kyoto Univ. Vol.43 No.3

      Pages: 235-265

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-14540151
  • [Journal Article] Missing terms in generalized Hardy's inequalities and its application.2003

    • Author(s)
      T.Horiuchi
    • Journal Title

      J.of Kyoto Univ. 43-3

      Pages: 235-265

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-15540153
  • [Journal Article] Missing terms in the weighted Hardy-Sobolev inequalities and its application

    • Author(s)
      安藤広、堀内利郎
    • Journal Title

      Journal of Mathematics of Kyoto Unuv. accepted

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20540153
  • [Journal Article] Kato's inequalities for degenerate quasilinear elliptic operators.

    • Author(s)
      T.Horiuchi, P.Kumlin
    • Journal Title

      Kungpook J. (in press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-17540144
  • [Journal Article] Kato's inequalities for degenerate quasilinear elliptic operators.

    • Author(s)
      T.Horiuchi, P.Kumlin
    • Journal Title

      Kungpook J. (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-17540144
  • [Journal Article] Kato's inequalities for degenerate quasilinear elliptic operators.

    • Author(s)
      T.Horiuchi, P.Kumlin
    • Journal Title

      Kungpook J. 印刷中

    • Data Source
      KAKENHI-PROJECT-17540144
  • [Presentation] The equivalences among p- capacity, p-Laplace-capacities and Hausdorff measure.2018

    • Author(s)
      Xiaojing Liu, Toshio Horiuchi
    • Organizer
      日本数学会、函数方程式分科会
    • Data Source
      KAKENHI-PROJECT-16K05189
  • [Presentation] The equivalences among p-capacity、p-Laplace-capacities and Hausdorff measure2018

    • Author(s)
      劉暁静、堀内利郎
    • Organizer
      日本数学会年会函数方程式分科会
    • Data Source
      KAKENHI-PROJECT-15H03621
  • [Presentation] Improved Kato's inequalities for a quasilinear elliptic operator and relating topics2018

    • Author(s)
      Toshio Horiuchi
    • Organizer
      ICM 2018 (Rio De Janeiro, Brasil)
    • Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-16K05189
  • [Presentation] Improved Kato's inequalities for a quasilinear elliptic operator and relating topics2018

    • Author(s)
      劉暁静、堀内利郎
    • Organizer
      Tsukuba Workshop for Young Mathematicians
    • Data Source
      KAKENHI-PROJECT-15H03621
  • [Presentation] p-ラプラシアンを含む精密化された加藤の不等式とその応用2017

    • Author(s)
      劉暁静、堀内利郎
    • Organizer
      日本数学会、函数方程式分科会
    • Place of Presentation
      首都大学東京
    • Year and Date
      2017-03-24
    • Data Source
      KAKENHI-PROJECT-16K05189
  • [Presentation] p-ラプラシアンを含む精密化された加藤の不等式とその応用2017

    • Author(s)
      劉暁静, 堀内利郎
    • Organizer
      日本数学会年会
    • Place of Presentation
      首都大学東京南大沢キャンパス
    • Year and Date
      2017-03-24
    • Data Source
      KAKENHI-PROJECT-15H03621
  • [Presentation] 加藤の不等式とその周辺2016

    • Author(s)
      堀内利郎
    • Organizer
      「偏微分方程式および関連する諸問題」研究集会
    • Place of Presentation
      茨城大学
    • Year and Date
      2016-09-10
    • Data Source
      KAKENHI-PROJECT-16K05189
  • [Presentation] Remarks on Kato's inequality when $\Delta_pu$ is a measure2016

    • Author(s)
      劉暁静、堀内利郎
    • Organizer
      日本数学会、函数方程式分科会
    • Place of Presentation
      関西大学
    • Year and Date
      2016-09-15
    • Data Source
      KAKENHI-PROJECT-16K05189
  • [Presentation] Remarks on Kato's inequality when Δp u is a measure2016

    • Author(s)
      劉暁静, 堀内利郎
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      関西大学
    • Year and Date
      2016-09-15
    • Data Source
      KAKENHI-PROJECT-15H03621
  • [Presentation] On Kato's inequalities when Δp u is a measure and related topics2016

    • Author(s)
      劉暁静, 堀内利郎
    • Organizer
      RIMS研究集会「偏微分方程式の解の形状解析」
    • Place of Presentation
      京都大学 数理解析研究所
    • Year and Date
      2016-11-09
    • Data Source
      KAKENHI-PROJECT-15H03621
  • [Presentation] Radial symmetry and its breaking in the Caffarelli-Kohn-Nirenberg type inequalities for p = 12015

    • Author(s)
      堀内利郎、千葉奈緒希
    • Organizer
      日本数学会(函数方程式分科会)
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-13
    • Data Source
      KAKENHI-PROJECT-24540157
  • [Presentation] p-ラプラシアンを含む強最大値原理についての注意2015

    • Author(s)
      劉暁静、堀内利郎
    • Organizer
      日本数学会(函数方程式分科会)
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-13
    • Data Source
      KAKENHI-PROJECT-24540157
  • [Presentation] Recent progress in Caffarelli-Kohn-Nirenberg inequalities2014

    • Author(s)
      Horiuchi Toshio
    • Organizer
      ICM 2014( International congress of Mathematician 2014 )
    • Place of Presentation
      Seoul Korea
    • Year and Date
      2014-08-21
    • Data Source
      KAKENHI-PROJECT-24540157
  • [Presentation] On the symmetry breaking of the non-critical Caffarelli-Khon-Nirenberg inequalities by a linearization method2012

    • Author(s)
      堀内利郎
    • Organizer
      日本数学会
    • Place of Presentation
      東京理科大
    • Year and Date
      2012-03-27
    • Data Source
      KAKENHI-PROJECT-20540153
  • [Presentation] On the Symmetry breaking of the non-critical Caffarelli-Khon-Nirenberg type inequalities by a linearization method2012

    • Author(s)
      T, Horiuchi
    • Organizer
      日本数学会
    • Place of Presentation
      東京
    • Year and Date
      2012-03-27
    • Data Source
      KAKENHI-PROJECT-20540153
  • [Presentation] 重み付きハーディの不等式の精密化に付いて2012

    • Author(s)
      安藤広、堀内利郎、中井英一
    • Organizer
      日本数学会
    • Place of Presentation
      東京
    • Year and Date
      2012-03-27
    • Data Source
      KAKENHI-PROJECT-20540153
  • [Presentation] Construction of slowly increasing functions2012

    • Author(s)
      安藤広、堀内利郎、中井英一
    • Organizer
      日本数学会
    • Place of Presentation
      東京
    • Year and Date
      2012-03-29
    • Data Source
      KAKENHI-PROJECT-20540153
  • [Presentation] On the Caffarelli-Kohn-Nirenberg type inequalities involving Critical and Supercritical weights2009

    • Author(s)
      T, Horiuchi
    • Organizer
      姫路研究集会
    • Place of Presentation
      姫路
    • Year and Date
      2009-02-21
    • Data Source
      KAKENHI-PROJECT-20540153
  • [Presentation] On the Caffarelli-Kohn-Nirenberg inequalities involving Critical and Supercritical weights2008

    • Author(s)
      堀内利郎
    • Organizer
      日本数学会2008年度秋期総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-24
    • Data Source
      KAKENHI-PROJECT-19540161
  • [Presentation] On the Caffarelli-Kohn-Nirenberg inequalities involving Critical and Supercritical weights2008

    • Author(s)
      堀内利郎
    • Organizer
      日本数学会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-24
    • Data Source
      KAKENHI-PROJECT-20540153
  • [Presentation] On the Caffarelli-Kohn-Nirenberg type inequalities involving Critical and Supercritical weights2008

    • Author(s)
      T, Horiuchi
    • Organizer
      日本数学会
    • Place of Presentation
      東京
    • Year and Date
      2008-09-24
    • Data Source
      KAKENHI-PROJECT-20540153
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  • 2.  ANDO Hiroshi (60292471)
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    # of Collaborated Products: 0 results
  • 17.  SADASUE Gaku (40324884)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 18.  SAWANO Yoshihiro (40532635)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 19.  MIZUTA Yoshihiro (00093815)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 20.  松久 富美子 (90194208)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 21.  初瀬 弘平 (10007552)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 22.  YAMAGAMI Shigeru (90175654)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 23.  OSHIMA Hideaki (70047372)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 24.  TAKANO Katsuo (30007827)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 25.  HORIHATA Kazuhiro (10229239)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 26.  NAKAZI Takahiko (30002174)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 27.  OZAWA Tohru (70204196)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 28.  中村 芳昭 (40007555)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 29.  薮田 公三 (30004435)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 30.  久保田 陽人 (30007538)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 31.  島倉 紀夫 (60025393)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 32.  西垣 誠一 (10180598)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 33.  米田 剛 (30619086)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 34.  倉坪 茂彦 (50003512)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 35.  藤間 昌一 (00209082)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 36.  宮地 晶彦 (60107696)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results

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